Tensor models (TMs) generalize matrix models and are considered as a convenient formalism for studying random
geometries [1]}-[2]}. TMs also offer an alternative to other approaches dealing with quantum gravity (QG) which is based on new mathematical/statistical tools, for example, the \(1/N\)  expansion recently discovered [3]}-[2]}. On the other hand, group field theory (GFT)
is a quantum field theory over group manifolds and is considered as a second quantization of
loop quantum gravity [5]}-[6]}. Both TMs and GFT belong to the so-called background-independent scenario for QG. They aim at describing a rudimentary phase of the geometry of spacetime, namely, when this geometry is hypothetically still in a discrete form, or at least not yet
continuous. It is also named "pre-geometric" phase of our spacetime. Recently TMs and GFT have
been combined to provide a new class of field theories so called tensorial group field theory (TGFT).
TGFTs improve the GFTs in order to allow for renormalization [7]}-[8]}. Moreover, it has been
shown that several TGFTs models are asymptotically free in the UV, in other words, near the Gaussian fixed point
[9]}-[10]}.
